Combinational circuit is a circuit in which we combine the different gates in the circuit, for example encoder, decoder, multiplexer and demultiplexer. Some of the characteristics of combinational circuits are following The output of combinational circuit at any instant of time, depends only on the levels present at input terminals. The combinational circuit do not use any memory. The previous state of input does not have any effect on the present state of the circuit. A combinational circuit can have an n number of inputs and m number of outputs. We're going to elaborate few important combinational circuits as follows. Half Adder Half adder is a combinational logic circuit with two inputs and two outputs. The half adder circuit is designed to add two single bit binary number A and B. It is the basic building block for addition of two single bit numbers. This circuit has two outputs carry and sum. Page 1
Circuit Diagram Full Adder Full adder is developed to overcome the drawback of Half Adder circuit. It can add two one-bit numbers A and B, and carry c. The full adder is a three input and two output combinational circuit. Page 2
Circuit Diagram Page 3
N-Bit Parallel Adder The Full Adder is capable of adding only two single digit binary number along with a carry input. But in practical we need to add binary numbers which are much longer than just one bit. To add two n-bit binary numbers we need to use the n-bit parallel adder. It uses a number of full adders in cascade. The carry output of the previous full adder is connected to carry input of the next full adder. 4 Bit Parallel Adder In the block diagram, A 0 and B 0 represent the LSB of the four bit words A and B. Hence Full Adder-0 is the lowest stage. Hence its C in has been permanently made 0. The rest of the connections are exactly same as those of n-bit parallel adder is shown in fig. The four bit parallel adder is a very common logic circuit. Page 4
N-Bit Parallel Subtractor The subtraction can be carried out by taking the 1's or 2's complement of the number to be subtracted. For example we can perform the subtraction (A-B) by adding either 1's or 2's complement of B to A. That means we can use a binary adder to perform the binary subtraction. 4 Bit Parallel Subtractor The number to be subtracted (B) is first passed through inverters to obtain its 1's complement. The 4-bit adder then adds A and 2's complement of B to produce the subtraction. S 3 S 2 S 1 S 0 represents the result of binary subtraction (A-B) and carry output C out represents the polarity of the result. If A > B then Cout = 0 and the result of binary form (A-B) then C out = 1 and the result is in the 2's complement form. Page 5
Half Subtractors Half subtractor is a combination circuit with two inputs and two outputs (difference and borrow). It produces the difference between the two binary bits at the input and also produces an output (Borrow) to indicate if a 1 has been borrowed. In the subtraction (A-B), A is called as Minuend bit and B is called as Subtrahend bit. Circuit Diagram Page 6
Full Subtractors The disadvantage of a half subtractor is overcome by full subtractor. The full subtractor is a combinational circuit with three inputs A,B,C and two output D and C'. A is the 'minuend', B is 'subtrahend', C is the 'borrow' produced by the previous stage, D is the difference output and C' is the borrow output. Circuit Diagram Page 7
Multiplexers Multiplexer is a special type of combinational circuit. There are n-data inputs, one output and m select inputs with 2m = n. It is a digital circuit which selects one of the n data inputs and routes it to the output. The selection of one of the n inputs is done by the selected inputs. Depending on the digital code applied at the selected inputs, one out of n data sources is selected and transmitted to the single output Y. E is called the strobe or enable input which is useful for the cascading. It is generally an active low terminal that means it will perform the required operation when it is low. Multiplexers come in multiple variations Page 8
2 : 1 multiplexer 4 : 1 multiplexer 16 : 1 multiplexer 32 : 1 multiplexer Block Diagram Demultiplexers A demultiplexer performs the reverse operation of a multiplexer i.e. it receives one input and distributes it over several outputs. It has only one input, n outputs, m select input. At a time only one output line is selected by the select lines and the input is transmitted to the selected output line. A de-multiplexer is equivalent to a single pole multiple way switch as shown in fig. Demultiplexers comes in multiple variations. 1 : 2 demultiplexer 1 : 4 demultiplexer Page 9
1 : 16 demultiplexer 1 : 32 demultiplexer Decoder A decoder is a combinational circuit. It has n input and to a maximum m = 2n outputs. Decoder is identical to a demultiplexer without any data input. It performs operations which are exactly opposite to those of an encoder. Page 10
Examples of Decoders are following. Code converters BCD to seven segment decoders Nixie tube decoders Relay actuator 2 to 4 Line Decoder The block diagram of 2 to 4 line decoder is shown in the fig. A and B are the two inputs where D through D are the four outputs. Truth table explains the operations of a decoder. It shows that each output is 1 for only a specific combination of inputs. Page 11
Logic Circuit Encoder Encoder is a combinational circuit which is designed to perform the inverse operation of the decoder. An encoder has n number of input lines and m number of output lines. An encoder produces an m bit binary code corresponding to the digital input number. The encoder accepts an n input digital word and converts it into an m bit another digital word. Page 12
Examples of Encoders are following. Priority encoders Decimal to BCD encoder Octal to binary encoder Hexadecimal to binary encoder Priority Encoder This is a special type of encoder. Priority is given to the input lines. If two or more input line are 1 at the same time, then the input line with highest priority will be considered. There are four input D 0, D 1, D 2, D 3 and two output Y 0, Y 1. Out of the four input D 3 has the highest priority and D 0 has the lowest priority. That means if D 3 = 1 then Y 1 Y 1 = 11 irrespective of the other inputs. Similarly if D 3 = 0 and D 2 = 1 then Y 1 Y 0 = 10 irrespective of the other inputs. Page 13
Logic Circuit Page 14
We discussed various combinational circuits in earlier chapters. All these circuits have a set of output(s), which depends only on the combination of present inputs. The following figure shows the block diagram of sequential circuit. Page 15